DE10236619A1 - Toroidal regulating device for toroidal gearbox ratio, particularly for motor vehicle, has single-loop control loop with regulator with differential elements in addition to proportional element - Google Patents

Abstract

The toroidal regulating device has a single-loop control loop with a regulator (R1) that has at least one differential element in addition to a proportional element. The regulator has at least one integral element whose lag time is greater than a regulator delay time. The integral element's lag time can be five times greater than the regulator's delay time. Independent claims are also included for the following: (a) a method of using an inventive toroidal regulating device (b) and a toroidal gearbox with an inventive toroidal regulating device.

Description

The invention particularly relates a toroidal control device according to the preamble of claim 1.

From the US 5,669,849 a toroidal control device for controlling a transmission ratio of a toroidal transmission is known. The toroidal control device has a first, electronic feedback system or a first control loop with a first controller, which provides feedback from a first physical characteristic, namely a pivot angle of an intermediate roller. Furthermore, the toroidal control device has a second electronic feedback system or a second control loop with a second controller, which provides feedback from a second physical characteristic of a rate of change of the swivel angle.

The invention is particularly the object of the invention to provide a Toroidregelvorrichtung, the at a low total design effort a particularly stable control behavior with a short settling time allows. It is according to the invention solved by the features of claim 1. Further embodiments emerge from the dependent claims and ancillary claims.

The invention is based on a Toroidal control device for controlling a transmission ratio a toroidal transmission, in particular a motor vehicle.

It is proposed that the toroidal control device has a single-loop control loop with a controller which has at least one differential element in addition to a proportional element. Poles, ie zeros of a denominator polynomial describing a controlled system, can be compensated with the aid of the D component. Using a small time constant T1, an additional pole in the left half plane of a plane spanned by an imaginary axis and a real axis can be placed at a large distance from the imaginary axis. It can be achieved a fast and very stable control. Furthermore, a derivative time T _{v of} the controller can be chosen freely in order to positively influence the control properties. A second feedback system or a second control loop with a second controller can be advantageously avoided. With a single regulator can advantageously in a Toroidgetriebe, especially in a Volltoroidgetriebe, a Castor angle, ie set an angle between a Zwischenrollerhalterung or an actuating piston of a Zwischenrollers and central shafts of the Toroidgetriebes equal to zero and yet a stable and fast control can be achieved. If the Castor angle can be set equal to zero or the adjusting piston of the intermediate roller can be made perpendicular to the central shafts of the toroidal transmission, in particular constructive effort and installation space can be saved. At a Castor angle equal to zero, compared to a non-zero Castor angle, no pivoting of the intermediate roller can be achieved in only one position, whereby a small stroke of the actuating piston can be achieved and energy can be saved.

To determine the controlled variable, various sensible to the person skilled in the art as meaningful state variables detected become more translation dependent and / or torque-dependent Can be nature such as a speed ratio, individual speeds, a swivel angle, a ratio change, a spin, a swivel angular velocity, an actuating velocity or more torque values, a control piston force, a pressure difference, a pressure change and / or a pressure difference change etc.

In a further embodiment of the Invention is proposed that the controller at least one Integral member has, whereby stationary control deviations at least can be largely avoided. It can in principle two poles are compensated. To achieve a particularly high stability, is advantageous a lag time of the integral term greater than a delay time of the controller, and indeed the follow-up time is at least a factor 5, advantageously by a factor of 10, greater than the delay time of the regulator. It can be advantageously achieved an attenuation greater than one.

Further advantages arise the following description of the drawing. In the drawing are exemplary embodiments represented the invention. The description and the claims contain numerous features in combination. The skilled person will become the characteristics expediently also consider individually and to meaningful further combinations sum up.

It shows:

1 a detail of a solid toroidal transmission shown schematically,

2 _{1 is} a block diagram of a first embodiment with a PDT ₁ controller,

3 a block diagram of a second embodiment with a PIDT ₁ controller,

4 a root locus for γ = 0, T _R = 0, T _V <T _S2 ,

5 a root locus for γ = 0, T _R = 0, T _V = T _S2 ,

6 a root locus for γ = 0, T _R = 0, T _V > T _S2 ,

7 a root locus for γ = 0, T _R = 0, T _V >> T _S2 ,

8th a root locus for γ = 0, T _R > 0,

9 a root locus for γ> 0, T _R = 0 and a pole position compensation,

10 a root locus for γ> 0, T _R = 0 and TV> -1 / s _p2,3 ,

11 a comparison of a reference variable behavior of a control loop with different Castor angles,

12 a root locus of a PIDT ₁ controller for γ = 0, T _R > 0

13 a root locus of a PIDT ₁ controller for γ = 0, T _R > 0

14 a comparison of a leadership behavior of the PIDT ₁ controller 11 and 13 for different jump heights and

15 a comparison of a control behavior of a control loop with a PIDT ₁ controller for γ = 0 and a PDT ₁ controller for γ = 5 with identical time delay T _R and gain K _R and matched derivative time T _V.

1 shows a section of a solid toroidal transmission of a motor vehicle shown schematically with a toroidal control device for controlling a transmission ratio. The solid toroidal transmission has one between two toroidal discs 12 . 13 arranged intermediate scooter 14 , whose pivot angle λ between the toroidal disks 12 . 13 via a hydraulic actuator 15 is adjustable. The actuator 15 has a valve block for this purpose 11 , about in a double-acting piston-cylinder unit 16 a pressure difference p ₁ -p _{2 is} adjustable. The piston-cylinder unit 16 is via a piston rod 17 with the intermediate scooter 14 connected, wherein via a force of the piston-cylinder unit 16 the piston rod 17 in the direction 18 . 19 displaced and thereby the swivel angle λ is adjustable. The piston rod 17 is perpendicular to central waves 20 . 21 aligned the Volltoroidgetriebes or the Volltoroidgetriebe has a Castor angle equal to zero.

According to the invention, the toroidal control device has a single-loop control loop with a regulator R _{1 which} , in addition to a proportional element PG, has a differential element DG ( 2 ). This is done by a sensor unit 10 the pivot angle λ detected, wherein the pivot angle λ and a command variable W are fed directly to the controller R ₁ .

The invention is based on the following Findings.

For the choice and design of a suitable regulator, it is favorable to use mathematical whole model, the individual elements the Volltoroidgetriebes in the form of transfer functions G maps. The considerations are made in the image area depending on the Laplace variable s.

The goal is the generation of an analytical total transfer function G of the least possible order with sufficient accuracy. A resulting controlled system RS is divided into individual partial control paths RS _a , RS _b , RS _c , since individual transmission elements between existing state variables must be known for the construction of different controls. In a first step, a dynamic behavior of the hydraulic controlled system RS _{a is to be represented} by means of a first transfer function G _S1 (s). In the second step, the description of a transfer function GS ₂ (s) of the mechanical controlled system RSb takes place, in which the influence of the castor angle γ must be considered. The interface forms an actuating piston of the piston-cylinder unit 16 , In the third and final step, the description of a transfer function G _S3 (s) of the controlled system RS _c , namely the coupling of speed ratio i and swing angle λ.

With regard to nomenclature, use is made of terms customary in control engineering. Quantities relating to the controller R ₁ are indicated by S, which refer to the controlled system RS.

For the controlled system RS _a in particular the properties of a control valve used are authoritative. For example, if this has a tightly tolerated, position-controlled control slide without overlapping of control edges, then the volume flow characteristic curve has a virtually linear course as a function of the manipulated variable y. Neglecting the dynamics of the control slide and response times, this results in a proportional transmission behavior. Furthermore, if a system without leakage is assumed, there will again be a proportional relationship between the volume flow and the translatory speed of the actuating piston as a result of the equation of continuity. Its location can be determined by integration. The transfer function G _S1 (s) thus corresponds to a pure integral term.

Als weitere Zustandsgröße des Zwischenrollers 14 wurde für die Regelstrecke RS_b der Schwenkwinkel λ eingeführt. Zur Ermittlung des Übertragungsverhaltens mit einer Eingangsgröße x, und zwar einem Stellweg des Stellkolbens der Kolben-Zylindereinheit 16, dient eine Bewegungsgleichung für die Schwenkbewegung des Zwischenrollers 14 als Basis. Werden die kinematischen Verhältnisse im Kontakt berücksichtigt, zeigt sich eine nichtlineare Beziehung zwischen einer Schwenkbeschleunigung und verschiedener Zustandsgrößen sowie deren Ableitungen,

(mit . ₁, . ₂: Drehzahlen der ersten und zweiten Toroidscheibe 12, 13).The hydraulic gain K _S1 in equation (1) is determined by a nominal volume flow Q _N , a nominal pressure drop Δp _N , an actual pressure drop Δp at the control edge of the control valve and a piston area A _{K of} the control piston and a maximum control variable y _max :

As a further state variable of the intermediate roller 14 was introduced for the controlled system RS _b the pivot angle λ. To determine the transmission behavior with an input variable x, namely a travel of the actuating piston of the piston-cylinder unit 16 , an equation of motion is used for the pivotal movement of the intermediate roller 14 as a base. If the kinematic relationships in the contact are taken into account, a non-linear relationship between a pivoting acceleration and various state variables and their derivatives is shown.

(with ₁ , ₂ : speeds of the first and second toroidal disc 12 . 13 ).

Therefore, in the next step, a linearization is performed around an operating point λ _s = 0 °. For a Castor angle γ> 0 °, a proportional transmission behavior results with a second-order delay, for a Castor angle γ = 0 ° an integrating behavior with a first-order delay.

The transfer function G _S2 (s) can be determined using the laws for interconnected control loop elements as follows:

In the following, it is assumed that a current coefficient of friction is always in the linear range of a friction-value slip curve. For a proportionality factor between coefficient of friction μ and slip s, a variable m _{μ is} introduced. Furthermore, let the rotary damping _{d4 of} the intermediate roller be 14 and a guide fork, not shown, proportional to the swivel speed, a parameter d _{4 is} used for this purpose.

(Index 1:
1: Toroidscheibe 12
2: Toroidscheibe 13
3: Zwischenroller 14 4: Führungsgabel/Kolbenstange 17,
mit RT_M: Toroidcenterkreisradius
R₃: Radius des Zwischenrollers 14
I₃: Trägheitsmoment des Zwischenrollers 14 um die Schwenkachse des Zwischenrollers 14
I₄: Trägheitsmoment der Führungsgabel/Kolbenstange 17 um die Schwenkachse des Zwischenrollers 14
f_n: Normalkraft im Kontaktpunkt)A time constant T _S2 and gain factors K _S2 and K _γ are defined as:

(Index 1:
1: toroidal disc 12
2: toroidal disc 13
3: intermediate scooter 14 4: Guide fork / piston rod 17 .
with RT _M : Toroidcenterkreisradius
R ₃ : radius of the intermediate roller 14
I ₃ : Moment of inertia of the intermediate roller 14 about the pivot axis of the intermediate roller 14
I ₄ : Moment of inertia of the guide fork / piston rod 17 about the pivot axis of the intermediate roller 14
f _n : normal force at the contact point)

For a Castor angle γ = 0 °, the constant K _γ becomes zero, cf. Equation (7). The transfer function G _S2 (s) of the mechanical controlled system RS _b is obtained from the equation (4) by extension with K _γ .

Finally, with regard to the controlled system RS _c, the relationship between the swivel angle λ and the speed ratio i is shown. Neglecting the slip, the following relationship exists:

eine gute Übereinstimmung mit Gleichung (8). Da in der Praxis ein deutlich größerer Verstellbereich genutzt wird, ist eine Linearisierung um verschiedene Arbeitspunkte durchzuführen. Alternativ kann anhand einer analytischen Gleichung – beispielsweise der Umkehrfunktion von Gleichung (8) – oder einer Näherungsfunktion ein korrelierender Schwenkwinkel λ bestimmt und als Regelgröße herangezogen werden.In a range approximately between -10 ° -λ + 10 °, the linearization around the operating point gives λ = 0 °

a good match with equation (8). Since a significantly larger adjustment range is used in practice, a linearization is to be performed at different operating points. Alternatively, based on an analytical equation - for example, the inverse function of equation (8) - or an approximation function, a correlating swing angle λ can be determined and used as a controlled variable.

The dynamic behavior of the whole Controlled system RS can now be approximated described by a few linear differential equations become.

The behavior of the controlled system G _s (s) results from the product of the sections RS _a , RS _b , RS _c :

eine von Null verschiedene Polstelle des offenen Regelkreises kompensiert werden kann. Der Regelkreis wird schneller, die Stabilität des Regelkreises verbessert. Ebenso ist es möglich, eine Vorhaltezeit T_V des Reglers R₁ frei zu wählen, um die Eigenschaften des geschlossenen Regelkreises positiv zu beeinflussen. Mittels einer Verzögerungszeit T_R des Reglers R₁ läßt sich die Lage einer Polstelle vorgeben und damit die Dynamik des Regelkreises gezielt beeinflussen.From the view of equation (11) it can be deduced that with the aid of the D-portion of the PDT ₁ controller R ₁

a non-zero pole of the open loop can be compensated. The control loop is faster, the stability of the control loop is improved. It is also possible to freely select a derivative time T _{V of} the regulator R _{1 in} order to positively influence the properties of the closed control loop. By means of a delay time T _{R of} the controller R ₁ , the position of a pole can be specified and thus influence the dynamics of the control loop targeted.

The transmission behavior of the open circuit is defined by:

There are four different cases become:

Case A: γ = 0, T _R = 0

The equation (12) reduces to:

A Polstellenkompensation is achieved by equating the lead time T _{V of} the controller R ₁ and the delay time T _S2 of the controlled system RS. The transfer behavior of the open loop results in an I ² element ( 5 ). The closed loop is independent of the overall gain K grenzstabil.

zeigt sich, daß dieser in der rechten Halbebene liegen wird, der Regelkreis somit instabil wird (4). Zum anderen besteht die Möglichkeit, die Vorhaltezeit T_V größer als die Zeitkonstante T_S2 zu setzen, wodurch der Wurzelschwerpunkt s_W in die linke Halbebene wandert. Der Regelkreis ist für eine Gesamtverstärkung K > 0 stabil (6). Daraus folgt, daß die Vorhaltezeit T_V möglichst groß zu wählen ist (7).If the derivative time T _V remains freely selectable, two cases must be distinguished. On the one hand, it is possible to set the derivative time T _V smaller than the time constant T _S2 . For example, based on the root gravity

shows that this will lie in the right half-plane, the control loop thus becomes unstable ( 4 ). On the other hand, it is possible to set the derivative time T _V greater than the time constant T _S2 , as a result of which the root center of gravity s _W travels to the left half-plane. The control loop is stable for a total gain K> 0 ( 6 ). It follows that the derivative time T _{V is} to be chosen as large as possible ( 7 ).

Case B: γ = 0, T _R > 0

For T _R > 0, the transmission behavior is as follows:

The delay time T _R is kept as small as possible, so that the pole of the closed loop adopts negative, as far as possible in terms of magnitude, real values.

Due to the three higher number from poles opposite Zeros result at the root locus for equation (15) the same number of asymptotes, which have an angle of 60 °, 180 ° and 270 ° to the Take real part axis.

In a pole position compensation, the transfer function G _o (s) of the open loop has the same structure as the unregulated controlled system RS. The nonzero pole moves to the left for T _R <T _S2 in the complex s plane. The exit angle of the branches from the double zero s _1,2 is too 5 identical, the control loop is unstable for K> 0.

If, as in case A, an increase of the derivative time T _{V is} performed, a stable behavior results for 0 <K <K _crit . Depending on the size of T _V and T _R damping D ≥ 1 can be realized. 8th shows the root loci for a desired design of the controller time constant. If the merge point is very close to the imaginary axis, the dynamic behavior of the system is sluggish with a design of D ≥ 1. A comparison with Case A shows that the delay time T _R reduces the speed of the control loop.

Case C: γ> 0, T _R = 0

Equation (12) provides:

The asymptotes run parallel to the imaginary axis. The root center of gravity s _W is not affected by the Castor angle γ. Equation (13) continues to apply. At T _V > T _S2 , the root gravity center s _{W is} again in the left half-plane, the system is stable for all overall gains K> 0. In the case of a pole position compensation pole and zero and the branch point of the root locus have the same ben value ( 9 ). An increase in the system dynamics can be achieved by increasing the derivative time T _V ( 10 ).

Case D: γ> 0, T _R > 0

The considerations are based on the transmission behavior according to equation (12). As in case B, there are three branches of the root locus that run to infinity. Instability occurs for large values of the overall gain K. The delay T _R > 0 also causes a shift of the branch point in the direction of imaginary axis compared to case C, the maximum possible settling time is reduced. Thus, the time constant is to be kept as small as possible.

Finally, a comparison of the reference variable behavior of the control loop with the controller R ₁ at different Castor angle γ is shown. The comparison basis is a controller with identical time delay T _R and gain K _R and matched derivative time T _V. Using a Castor angle γ ≠ 0, an ideal course can be achieved at the swivel angle λ, for γ = 0, a similarly good behavior results ( 11 ). Characteristic features of the analyzed controller designs are a slight overshoot and low steady-state deviations. This in 11 shown timing initially shows an asymptotic approaching the intermediate roller 14 to the new setpoint value, however, after a few seconds, the mentioned control deviation.

In principle, by increasing the delay time T _R, the stationary control deviation can be reduced, the control loop is faster with otherwise identical design, the lead time T _V is adjusted.

um stationäre Regelabweichungen zu beseitigen bzw. zu verhindern. 3 shows an alternative Toroidregelvorrichtung with a controller R ₂ , which in addition to a proportional element PG and a differential element DG DG has an integral term IG, in additive form according to the equation

to eliminate or prevent stationary control deviations.

Substantially constant components are basically numbered with the same reference numerals.

A case distinction between T _R = 0 and T _R > 0 is no longer made, the effects have already been shown above using the regulator R ₁ .

Case A: γ = 0

First, consider the simplified case for K _γ = 0. The transfer function G _R (S) of the open loop is:

The system has a threefold zero in the coordinate origin. If a pole-position compensation is performed with a follow-up time T _N > 0 and a derivative time T _V > 0, two of the three branches of the root locus for K> 0 always have positive real parts independently of T _R , the system is unstable.

möglichst weit in der linken Halbebene zu plazieren, die Zeitkonstanten T_V und T_N sind groß zu wählen, die Verzögerungszeit T_R ist klein zu halten.For the stability of the system is the root focus

as far as possible to place in the left half-plane, the time constants T _V and T _N are large to choose, the delay time T _R is to be kept small.

For K> K _crit , the system is stable, and a design with maximum control loop dynamics and a damping of one is possible ( 12 and 13 ). In 14 By way of example, a comparison of the reference variable behavior of the toroidal transmission for different jump heights is given. This shows a low dependence on the jump height. The dynamic behavior has been optimized for a jump height of + 10 °. Stationary control deviations, as they occur when using a PDT ₁ controller can thus be completely eliminated by means of the integral term IG.

For other setpoint changes show up first Deviations due to the low integral part only be corrected very slowly. At smaller jump heights will the new setpoint exceeded, fell below at higher jump heights. By consideration the jump height with the controller parameters an elimination of the influence is possible.

Case B: γ> 0

lassen sich theoretisch zwei von null verschiedene Polstellen mit Hilfe der beiden Zählernullstellen des Reglers R₂ kompensieren. Wird dieses Verfahren in entsprechender Weise durchgeführt, so ergibt sich ein Übertragungsverhalten des offenen Regelkreises zu:

According to equation (20)

theoretically two non-zero poles can be compensated with the help of the two counter zeros of the regulator R ₂ . If this procedure is carried out in a corresponding manner, the result is a transmission behavior of the open control loop to:

If the associated root locus is determined again, it becomes clear that the system is unstable for K> 0. Using an ideal PID controller with no time delay (T _1R = 0) eliminates the left branch of the root locus, the system becomes borderline stable.

Next, the control behavior when using a PIDT ₁ controller according to equation (17) will be examined, wherein only one pole of the controlled system is compensated.

If one considers the system behavior using an ideal PID controller, the following variants result for the root locus curves T _R = 0, T _V <T _S2 , T _V = T _S2 , T _V > T _S2 , T _V >> T _S2 , (see . 4 - 8th ). The branch, starting in the non-zero pole, always runs to the zero point, the other two branches strive towards infinity. For the stability of the system, it is necessary to place the zero between the poles. Thus, the follow-up time T _N must always be greater than the resulting time delay T _1R the controlled system RS, preferably at least by a factor of 10. Again, it is very clear that the integrating portion of the regulator R _2, the system in principle adversely affected and therefore be kept to a minimum or should be eliminated.

For real PID controllers with first-order lag, the system receives another pole, the desired root locus corresponds to the representation in 8th , It is confirmed the finding that the delay T _{R should be} small compared to the delay of the controlled system, otherwise there is a vibratory system.

Finally, the general system behavior without poling compensation should be considered. Based on the findings of Case A, the two zeros are again placed between the largest non-zero pole and the origin. The root loci are the in 12 and 13 very similar to the progressions shown. Due to the reduced by one number of poles in the origin of the branch of the root locus between origin and zero deleted. Furthermore, the merge point is no longer left of the two zeros, but in between.

As with a PDT ₁ controller for variators or toroidal transmissions with a Castor angle γ = 0, the integrating component leads to an overshoot of the controlled variable.

On the basis of the above considerations, it follows that using an integral governor portion in solid toroidal transmissions with a Castor angle γ not equal to zero, the dynamics of a full toroidal transmission with a castor angle equal to zero can be modeled. In the case of two compensated poles, the transmission behavior is equivalent to a control loop with P-controller, and in the case of a compensated pole, a loop with a PDT ₁ controller.

From a Polstellenkompensation is generally foreseeable because instability or limit stability of the system can occur. Furthermore, a more favorable system behavior can always be achieved with free choice of the pole. The delay time T _R is to be kept as low as possible, since this adversely affects the system behavior with increasing value. The damping of the control loop is reduced, depending on the control loop vibrations occur from a limit.

For toroidal gears with a Castor angle γ> 15 °, a P-controller is sufficient. At lower Castor angle γ, a PDT ₁ controller should be used, which generates sufficient system damping electronically. For toroidal gears without castor angle γ, a PIDT ₁ controller shows the best features.

Finally, a comparison of the reference variable behavior of the two established control loops with the regulator R ₁ in a toroidal transmission with a Castor angle γ ≠ 0 or with the controller R ₂ in the illustrated Volltoroidgetriebe without Castor angle γ or with a Castor angle given γ = 0. 15 shows that a very similar dynamic behavior can be achieved only by adjusting the attenuation and using an I component.

10

sensor unit

11

manifold

12

toroidal

13

toroidal

14

between Roller

15

actuator

16

Piston-cylinder unit

17

piston rod

18

direction

19

direction

20

central shaft

21

central shaft

PG

proportional element

DG

differentiating element

IG

integrating means

T _N

Follow-up time

T _1R

Delay Time

T _V

Derivative

λ

state variable

W

command variable

γ

Castor angle

G _R1

transfer function

G _R2

transfer function

G _S

transfer function

R ₁

regulator

R ₂

regulator

RS

controlled system

p ₁

pressure

p ₂

pressure

Claims (6)

Toroidal control device for controlling a transmission ratio of a toroidal transmission, in particular of a motor vehicle, characterized by a einschleifigen control circuit with a controller (R ₁ , R ₂ ), in addition to a proportional element (PG) at least one differential element (DG). Toroidal control device according to Claim 1, characterized in that the controller (R ₂ ) has at least one integral element (IG). Toroidal control device according to claim 2, characterized in that an after-running time (T _N ) of the integral element (IG) is greater than a delay time (T _1R ) of the regulator (R2). Toroidal control device according to claim 3, characterized in that the follow-up time (T _N ) min at least by a factor of 5 is greater than the delay time (T _1R ) of the controller (R ₂ ). Method with a toroidal control device according to one of the preceding claims, wherein - at least one state variable (λ) correlating with a transmission of the toroidal transmission via a sensor unit ( 10 ) is detected and - the state variable (λ) and a reference variable (W) indirectly in a modified form or directly to the controller (R ₁ , R ₂ ) are supplied. Toroidgetriebe with a toroidal control device according to one of previous claims with a Castor angle (γ) equals zero.